TY - GEN
T1 - Designing single- and multiple-shell sampling schemes for diffusion MRI using spherical code
AU - Cheng, Jian
AU - Shen, Dinggang
AU - Yap, Pew Thian
PY - 2014
Y1 - 2014
N2 - In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not directly related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the continuous unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).
AB - In diffusion MRI (dMRI), determining an appropriate sampling scheme is crucial for acquiring the maximal amount of information for data reconstruction and analysis using the minimal amount of time. For single-shell acquisition, uniform sampling without directional preference is usually favored. To achieve this, a commonly used approach is the Electrostatic Energy Minimization (EEM) method introduced in dMRI by Jones et al. However, the electrostatic energy formulation in EEM is not directly related to the goal of optimal sampling-scheme design, i.e., achieving large angular separation between sampling points. A mathematically more natural approach is to consider the Spherical Code (SC) formulation, which aims to achieve uniform sampling by maximizing the minimal angular difference between sampling points on the unit sphere. Although SC is well studied in the mathematical literature, its current formulation is limited to a single shell and is not applicable to multiple shells. Moreover, SC, or more precisely continuous SC (CSC), currently can only be applied on the continuous unit sphere and hence cannot be used in situations where one or several subsets of sampling points need to be determined from an existing sampling scheme. In this case, discrete SC (DSC) is required. In this paper, we propose novel DSC and CSC methods for designing uniform single-/multi-shell sampling schemes. The DSC and CSC formulations are solved respectively by Mixed Integer Linear Programming (MILP) and a gradient descent approach. A fast greedy incremental solution is also provided for both DSC and CSC. To our knowledge, this is the first work to use SC formulation for designing sampling schemes in dMRI. Experimental results indicate that our methods obtain larger angular separation and better rotational invariance than the generalized EEM (gEEM) method currently used in the Human Connectome Project (HCP).
UR - http://www.scopus.com/inward/record.url?scp=84906973290&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-10443-0_36
DO - 10.1007/978-3-319-10443-0_36
M3 - Conference contribution
C2 - 25320810
AN - SCOPUS:84906973290
SN - 9783319104423
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 281
EP - 288
BT - Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014 - 17th International Conference, Proceedings
PB - Springer Verlag
T2 - 17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014
Y2 - 14 September 2014 through 18 September 2014
ER -